We observe that the condition C1 is very mild since any solution \((u,\rho )\)  of the system (REF ) such that \(u(t,\cdot )\in C^1(\mathbb {E})\)  and \(\rho (t,\cdot )\in C^0(\mathbb {E})\)  satisfies it. In particular, the existence and uniqueness results proved in [1]}, [2]}, [3]}, [4]} fulfill such requirement.
